Geodesic behavior for Finsler metrics of constant positive flag curvature on S2
We study non-reversible Finsler metrics with constant flag curvature 1 on S2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1- parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metric with constant positive flag curvature is completely integrable. Finally, we give an example of a Finsler metric on S2with positive flag curvature such that no two closed geodesics intersect and show that this is not possible when the metric is reversible or has constant flag curvature.
Bryant, RL; Foulon, P; Ivanov, SV; Matveev, VS; Ziller, W
Volume / Issue
Start / End Page
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)